Is it the box, the splitter, the outside line, static, gremlins?

We paid comcast to send technicians out to switchover 3 TV's. Two are on adapters and one is on a box. The two on adapters work fine. The one on the box has to "reboot" 4 times when we turn it on (after being off for several hours). The TV stays on, but the box turns off, then on, etc. So far, technicians have been out twice and replaced the box and power booster for the box. They want to come out to dig in a new line outside, but could it be a problem with our splitter? It always worked before. Do we need a different kind of splitter?